In the above definitions, the constructed graph \(G\)  is assumed to be fully connected, meaning that each vertex is connected to all other vertices in \(G\) . In this case, the computational load for the minimizations of Eq. (REF ) and Eq. (REF ) will be extremely heavy. Spectral graph theory [1]}, [2]} or nearest neighbour [3]}, [4]} techniques are typically employed to limit the number of edges that are considered. For example, [1]} and [2]} use spectral approaches and the Nystrom extension method [7]} to efficiently calculate the eigen-decomposition of a dense graph Laplacian. In this work, we build the graph by borrowing the positions of the vertices and the connectivity between vertices in the finite element mesh as the vertices and edges in the graph. With this structure, the graph is sparsified and only connected vertices for a given vertice are taken into consideration. In such a case, Eq. (REF ) and Eq. (REF ) are equivalent to
\( \left\Vert  {\nabla _w} \mu \right\Vert _1 = \sum \limits _{i =1}^{N} {\sum \limits _{j \in {\cal N}_i} {\left| {\left( { {\mu _j} - {\mu _i}} \right)\sqrt{{w_{ij}}} } \right|} },\) 
